Theorems · Theorem · field theory
IntermediateField.le_normalClosure
∀ {F : Type u_1} {L : Type u_3} [inst : Field F] [inst_1 : Field L] [inst_2 : Algebra F L] (K : IntermediateField F L),
K ≤ IntermediateField.normalClosure F (↥K) L- Defined in
- Mathlib.FieldTheory.Normal.Closure
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement and proof · cited by 988
- Eq.trans_leproof · cited by 155
- IntermediateField.valproof · cited by 42
- IntermediateField.normalClosurestatement · cited by 38
- IntermediateField.fieldRange_valproof · cited by 9
- AlgHom.fieldRange_le_normalClosureproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- IntermediateField.normal_iff_normalClosure_leproof · cited by 3
- IntermediateField.normalClosureOperatorproof · cited by 2
- krullTopology_mem_nhds_one_iff_of_normalproof · cited by 1
- InfiniteGalois.isOpen_iff_finiteproof · cited by 1
- IsGalois.finiteDimensional_of_finiteproof · cited by 1
- FiniteGaloisIntermediateField.subset_adjoinproof · cited by 1
- separableClosure.normalClosure_eq_selfproof · cited by 0
- algebraicClosure.normalClosure_eq_selfproof · cited by 0
- InfiniteGalois.fixingSubgroup_fixedFieldproof · cited by 0